The short way to do this is to figure out that there is no perfect publisher for everything. If you write in only one genre then you're fairly set. There are plenty of publishers for that one genre and if that works for you then go for it. Personally the idea of having all of my books with one publisher is not only impossible because of the different genres I write in but also it simply won't be happening and the idea is frightening.
I'm currently with seven publishers because each offers me something different. That number will go down and there are a few that I only have one or two things with but the point is that I tried them out and figured out what I liked and maybe what I didn't.
Talking to authors is critical if you want to figure out if a publisher would be a good fit for you. Check for authors that you've heard of and that have multiple books with the publisher. Not just a series but multiple books because series often come with the right of first refusal so that doesn't absolutely mean that the author is happy, it could just mean that they wanted to get the series out for the readers.
Assuming that you've talked to authors and got some good recommendations from them about the publisher you want to be with now is the time to check out their anthology submission calls. These are simple, quick ways to see if you like working with a publisher before giving them an entire novel that they have the contract to for the next few years.
Assuming all goes well with the anthology then feel free to jump in with a series or send them a single. I'm more comfortable with singles than series just because a single I can walk away from if things go south. A series I'm tied to.
These are things that I look for when choosing a publisher. Its not just about the sales numbers, though of course you want to sell books and that's sort of the whole point of this. Here's what else helps to decide on which publisher to go with-
Do you know their name? Think about it, if you've never bought a book from them you might not want to be writing for them.
Do they have any scandals? This isn't an absolute no-go but it could be a big warning sign depending on what it was.
How are their covers? People will often buy books based on covers. Some publishers have less than great covers and still have great sales but its a rare combination.
How is their editing? Grab one of their books and give it a go. If they're sloppy you'd probably be better staying away because readers will too.
What is their online appearance? Are the owners nice online via facebook and twitter? Do they interact with readers? If they have no online connection you're probably better staying away.
Do they have awards? Every genre has awards and the publishers that have books that get them start to look pretty good. Its not a guarantee of course but it can be a reflection of quality.
How do they treat you as an author? Now that you're with them, expect to be treated well. You may not be the prized pony in their stable but your emails should be answered promptly and their editors should treat you with respect. Anything else is a red flag.
Do they do events? Not every smaller publisher is at the big reader conventions but a lot of the larger publishers are and it shows that they're interested in making a connection with readers.
Find out what the distribution channels are for the publisher. Amazon, ARe, Bookstrand. There are lots of places and if your book is in them there is a greater likelihood for more sales.
Unless you're looking at a vanity press you should never be paying anything for your book to be published at any step of the way.
Look at the reviews for some of their books. Do they have a lot of reviews? That means people are reading their books. Generally positive reviews? People are liking their books.
Hope this helped. There is not one, perfect, absolute publisher for each person. And plenty of people are with more than one. But knowing what to look out for can help steer you toward a better publisher.